On the distance and algorithms of strong product digraphs

TL;DR

This paper investigates the distance and average distance in strong product digraphs, providing formulas and algorithms to analyze their structural properties and implications for network communication efficiency.

Contribution

It introduces a formula for the distance and an algorithm for the average distance in strong product digraphs, advancing understanding of their structural and network properties.

Findings

Derived a formula for the distance of strong product digraphs.

Developed an algorithm to compute the average distance in these digraphs.

Enhanced analysis of interconnection network performance based on digraph distances.

Abstract

Strong product is an efficient way to construct a larger digraph through some specific small digraphs. The large digraph constructed by the strong product method contains the factor digraphs as its subgraphs, and can retain some good properties of the factor digraphs. The distance of digraphs is one of the most basic structural parameters in graph theory, and it plays an important role in analyzing the effectiveness of interconnection networks. In particular, it provides a basis for measuring the transmission delay of networks. When the topological structure of an interconnection network is represented by a digraph, the average distance of the directed graph is a good measure of the communication performance of the network. In this paper, we mainly investigate the distance and average distance of strong product digraphs, and give a formula for the distance of strong product digraphs and an algorithm for solving the average distance of strong product digraphs.